We have arrived at number one, Harry Potter and the Prisoner of Azkaban. Although there may have been some twists and turns, it is pretty much widely accepted that this is the best Harry Potter film, and it is hard to argue with that.
Prisoner of Azkaban the book is widely appreciated as well, but personally it wouldn't be in my top three (or maybe even four). The movie, and this list, is a different story. It's the lowest grossing film in the series, but it also has the second highest Rotten Tomatoes rating and the most acclaimed director at the helm.
In the first two films we are frightfully aware that the stars of the films are child actors, even when they are doing a good job we are aware of their technique. Radcliffe has personally said several times that Cuaron (director of great films like Children of Men and Y tu Mama Tambien) helped him become a better actor, and it shows in this movie. Radcliffe, Watson, and Grint are each in top form here, and they come to fully realize their roles.
Also, Michael Gambon took over the role of Dumbledore after the death of the previous actor who played Dumbledore Richard Harris. Initially I was reticent to accept this newer and more active headmaster, the fact that he was intentionally involving himself and being so blase towards Harry made me think that he was more fallible than the wise and distanced character played by Harris. But upon repeat viewings he really grew on me, and he turned out to be the perfect man to play the Dumbledore of the later films (particularly The Half-Blood Prince). People can talk about the convenience of a time turner, or how time travel deeply impacts the rest of the series, but that doesn't make the film less enjoyable.
The movie is about redemption; heavy ideas are conveyed over its 142 minute running time without pandering to its youth audience. And despite not featuring the big bad Voldemort, it's not like nothing happens: Sirius is redeemed as the innocent prisoner, Harry finally comes to terms with the death of his parents after he realizes he was the one with the stag patronus, werewolves and dementors are introduced into the universe, and the Marauder's Map makes its way into the dastardly hands of those without the necessary permission slips.
The Prisoner of Azkaban wasn't only a great movie, it paved the way for all of the other great Harry Potter movies. It was relatively faithful to the book, but it was still suspenseful for the people who read it. Alfonso Cuaron only directed one Harry Potter movie, but he certainly left his stamp on the franchise. Hopefully while you were reading this list you decided to watch all of the movies again to see if the list holds up, because you should. My boggart is a world without Harry Potter.